Logic in Classical Indian Philosophy

The exercise of reasoning and the practice of argument are recorded in
the early texts of India. Preoccupation with the nature of reason and
argument occurs in the earliest philosophical texts, where their
treatment is intimately connected with questions of ontology,
epistemology and dialectics. These questions continued to be at the
center of philosophical discussion through the classical and medieval
period of Indian philosophy. This article will chronicle the answers
Indian philosophers gave to these questions during the pre-classical
and classical period.

1. Reasoning and Logic

Humans reason: that is, taking some things to be true, they conclude
therefrom that other things are also true. If this is done in thought,
one performs an inference; and if this is done in speech, one makes an
argument. Indeed, inference and argument are but two sides of the same
coin: an argument can be thought, and hence become an inference; an
inference can be expressed, and hence become an argument.

Logic, at least as traditionally conceived, seeks to distinguish good
reasoning from bad. More particularly, it seeks to identify the
general conditions under which what one concludes is true, having
taken other things to be true. These conditions can be sought in the
nature of things. One asks, then, under what conditions do certain
facts require some other fact. This perspective on reasoning is an
ontic perspective. Next, insofar as facts are grasped in thought, one
can also ask under what conditions does knowledge of some facts permit
knowledge of another fact. Such conditions, once identified, would
distinguish good inferences from bad inferences. This perspective on
reasoning is an epistemic one. A third perspective is a dialectic one.
After all, insofar as facts have been stated, one can ask as well
under what conditions does the acceptance by someone of some facts
require him or her to accept some other fact. These conditions, once
identified, would distinguish good arguments from bad arguments.
Finally, since an argument is an expression of an inference, and to
that extent, expressed in a language, it is natural to use the forms
of linguistic expressions to identify forms of inferences and
arguments and thereby to distinguish forms of good inferences and
arguments from forms of bad inferences and arguments. This perspective
is a linguistic one. The study of reasoning in India has been from the
ontic, epistemic and dialectic perspective, and not from the
linguistic perspective, the perspective best known to modern
thinkers.

2. Pre Classical Period

The fact that humans reason is no guarantee that those who do reflect
on which reasoning is good and which is bad. Clearly, the activity of
reasoning, on the one hand, and the activity of reflecting on which
reasoning is good and which is not, on the other, are distinct, though
naturally they are intimately related. The exposition here, while
reporting primarily on what is explicit, will also report on what is
implicit. In looking at the origins of reasoning in India, it is
natural to begin with the practices in which reasoning played a role
and which, as a result, were likely candidates for reflection. The
obvious starting points for such practices are all forms of rational
inquiry.

Rational inquiry comprises the search for reasons for publicly
accepted facts, subject to public and rational scrutiny. This activity
involves people both severally and collectively. It involves people
severally insofar as people, individually, are the locus of inference.
It involves people collectively insofar as arguments, the public
manifestation of inferences, are sharpened by the scrutiny of
others.

Though the origins in India of public debate (pariṣad),
one form of rational inquiry, are not clear, we know that public
debates were common in pre-classical India, for they are frequently
alluded to in various Upaniṣads and in the early
Buddhist literature. A better known, but much later, example of such
engagements is the Buddhist works, Milinda-pañho
(Questions of King Milinda) and Kathā-vatthu
(Points of controversy).

Public debate is not the only form of public deliberations in
pre-classical India. Assemblies (pariṣad or
sabhā) of various sorts, comprised of relevant experts,
were regularly convened to deliberate on a variety of matters,
including administrative, legal and religious matters. As reported by
Solomon (1976: ch. 3), much of the legal vocabulary for such
deliberations includes the well-known terms of debate and argument
found in the philosophical literature (see also Preisendanz 2009).

By the fifth century BCE, rational inquiry into a wide range of topics
was under way, including agriculture, architecture, astronomy,
grammar, law, logic, mathematics, medicine, phonology and statecraft.
Aside from the world’s earliest extant grammar,
Pāṇini’s
Aṣṭādhyāyī, however, no works
devoted to these topics actually date from this pre-classical period.
Nonetheless, scholars agree that incipient versions of the first
extant texts on these topics were being formulated and early versions
of them were redacted by the beginning of the Common Era. They include
such texts as Kṛṣi-śāstra (Treatise
on agriculture), Śilpa-śāstra
(Treatise on architecture),
Jyotiṣa-śāstra (Treatise on
astronomy), Dharma-śāstra (Treatise on
law), Caraka-saṃhitā (Caraka’s
collection), a treatise on medicine, and
Artha-śāstra (Treatise on wealth), a
treatise on politics.

3. Early Classical Period

The first five hundred years of the Common Era also saw the redaction
of philosophical treatises in which proponents of diverse
philosophical and religious traditions put forth systematic versions
of their world view. These latter works bear witness, in a number of
different ways, to the intense interest in argumentation during this
period. This interest reveals itself in three different ways. First,
authors made arguments which correspond to well-known forms of logical
argument. Second, authors used or adduced logical principles of
reasoning such as the principle of non-contradiction, the principle of
excluded middle and the principle of double negation. Third, some
authors isolated canonical forms of argument.

3.1 Reasoning Used

Many of the arguments formulated in these texts correspond to such
well recognized rules of inference as modus ponens (i.e.,
from \(\alpha\) and \(\alpha\rightarrow \beta\), one infers
\(\beta\)), modus tollens (i.e., from \(\neg \beta\) and
\(\alpha\rightarrow \beta\), one infers \(\neg \alpha\)),
disjunctive syllogism (i.e., from \(\neg \alpha\) and
\(\alpha\lor \beta\), one infers \(\beta\)), constructive
dilemma (i.e., from \(\alpha\lor \beta\), \(\alpha\rightarrow
\gamma \) and \(\beta\rightarrow \gamma \), one infers \(\gamma \)),
categorical syllogism (i.e., from \(\alpha\rightarrow \beta\)
and \(\beta\rightarrow \gamma \), one infers \(\alpha\rightarrow
\gamma \)) and reductio ad absurdum (i.e., if something false
follows from an assumption, then the assumption is false). This last
form of argument, termed prasaṅga in Sanskrit, was
extremely common. Indeed, so common are such arguments in the works of
the Buddhist philosopher Nāgārjuna (2nd century
CE) that his follower, Buddhapālita (470–540), took all of
Nāgārjuna’s arguments to be prasaṅga
arguments. As a result, Buddhapālita and his followers were, and
are, referred to as prāsaṅgikas, or
absurdists.

3.2 Principles Used

Though no author of classical India made the principle of
non-contradiction an object of study, it was almost always
presupposed. Thus, for example, in the Samyutta Nikāya
(Collection of short discourses 4.298, 4.299), from the
Buddhist Tri-piṭaka, one finds someone known as
Nigaṇṭha Nātaputta saying: “See how upright,
honest and sincere Citta, the householder, is”; and, a little
later, he also says: “See how Citta, the householder, is not
upright, honest or sincere.” To this, Citta replies: “if
your former statement is true, your latter statement is false and if
your latter statement is true, your former statement is
false.”

Explicit formulations of the ontic principle of non-contradiction are
found very early in the philosophical literature. Thus, the Buddhist
philosopher Nāgārjuna (c. 2nd century CE) often
invokes an ontic principle of non-contradiction, saying such things as
“when something is a single thing, it cannot be both existent
and non-existent”
(Mūla-madhyamaka-kārikā (Basic verses on
the middle way) MMK 7.30), clearly reminiscent of
Aristotle’s own ontic formulation of the principle of
non-contradiction, namely, “that a thing cannot at the same time
be and not be” (Metaphysics: Bk. 3, ch. 2,
996b29–30). Nor are such formulations rare. Vātsyāyana
(5th CE), in his Nyāya-bhāṣya
(Commentary on logic), says:

Moreover, because of the exclusivity of being eternal and being
non-eternal, eternality and non-eternality must be excluded as two
properties of the very same property-possessor. (That is,) they cannot
occur together. (comment to NS 5.1.36)

Bhartṛhari (6th CE), the eminent grammarian and
philosopher of language, formulates an ontic version of the principle
of excluded middle in his Vākyapadīya (On
sentences and words), saying “A thing must be either
existent or non-existent: There is no third” (VP 3.9.85).

Like Aristotle, classical Indian thinkers were aware of the possible
limitation of the principle of excluded middle. Candrakīrti, for
example, in his Prasannapadā (Clear-worded
(commentary)), a commentary to Nāgārjuna’s
Mūla-mādhyamaka-kārikā, points out that
incompatible properties fail equally to apply to non-existent
objects.

But to some who have acquired a clear view of truth through very long
practice and by whom the roots of the trees of obstruction have been
unuprooted by only a little, it has been taught that it is neither
true nor untrue; in order to destroy the least obstruction, both have
been denied, just as one denies both whiteness and blackness of the
son of a barren woman. (comment to MMK 8.18; cited by Staal 1975: 43;
reprint, p. 50)

Finally, in classical India, one finds ontic formulations of the
principle of double negation. Vātsyāyana says: “It is
well known that the absence of those things which exist is
excluded” (commentary to NS 2.2.10).

3.3 Arguments with Form

Awareness of the fact that the form of argument is crucial to its
being good is found in a Buddhist work of the third century BCE,
Moggaliputta Tissa’s Kathā-vatthu, in which is
found the refutation of some two hundred propositions over which the
Sthaviravādins, one of the Buddhist schools, disagreed with other
Buddhist schools. The treatment of each point comprises an exchange
between a proponent and an opponent. The refutations, of course, turn
on demonstrating the inconsistency of a set of propositions. For
example, in the passage below, the Sthaviravādin questions his
opponent, here a Pudgalavādin, about whether or not the soul is
known truly and ultimately.

Sthaviravādin:
Is the soul known
truly and ultimately?

Pudgalavādin:
Yes.

Sthaviravādin:
Is the soul known
truly and ultimately just like any ultimate fact?

Pudgalavādin:
No.

Sthaviravādin:Acknowledge
your
refutation,
If the soul is known truly and ultimately, then indeed, good sir, you
should also say that the soul is known truly and ultimately just like
any ultimate fact.
What you say here is wrong: namely, that we ought to say (a)
that the soul is known truly and ultimately; but we ought not to say
(b) that the soul is known truly and ultimately just like any ultimate
fact. If the
latter statement (b) cannot be admitted, then indeed the former
statement (a) should not be admitted. It is wrong to affirm the former
statement (a) and to deny the latter (b).

One easily abstracts from this the following form,

Sthaviravādin:
Is AB?

Pudgalavādin:
Yes.

Sthaviravādin:
Is CD?

Pudgalavādin:
No.

Sthaviravādin:
Acknowledge your
refutation,
If A is B, then C is D.
What you say here is
wrong: namely, (a) that A is B but that C is not
D.
If C is not D, then A is not B. It is wrong that
A is B and C is not D.

Indeed, this form is repeatedly instantiated throughout Book 1,
Chapter 1.

Clearly, the author takes for granted the following: first, that the
propositions assented to are inconsistent, satisfying the following
inconsistent propositional schemata of \(\alpha\) , \(\neg \beta\) ,
\(\alpha\rightarrow \beta\); second, that it is wrong to hold
inconsistent propositions; and, third, that if \(\alpha\rightarrow
\beta\), then \(\neg \beta \rightarrow \neg \alpha\)—that is,
half of the equivalence of the principle of contraposition.

The earliest passages concerned with argument and inference are found,
on the one hand, in the philosophical literature, both Brahmanical and
Buddhist, and, on the other, in Caraka-saṃhitā, a
medical text, conjectured by some to have been redacted in its current
form at the beginning of first century CE. The best known Brahmanical
text pertaining to inference is Nyāya-sūtra
(Aphorisms on logic) by Gautama, also known as
Akṣapāda (c. 2nd CE), a treatise on rational
inquiry, whose actual redaction is thought by some to date to the
third century CE. Two other Brahmanical works which touch on inference
are Vaiśeṣika-sūtra (Aphorisms on
individuation), a treatise of speculative ontology attributed to
Kaṇāda (c. 1st century CE), and
Ṣaṣṭi-tantra (Sixty doctrines),
attributed by some to Pañcaśikha (c. 2nd
century BCE) and by others to Vrṣagaṇa (c. after the
2nd century CE), and surviving only in fragments.

The remaining texts are found in the Buddhist philosophical
literature. An early Buddhist text of unknown authorship, whose
original Sanskrit has been lost, but whose translations into Tibetan
and Chinese have been preserved, is
Sandhi-nirmocana-sūtra (Aphorisms on release from
bondage). The earliest identified Buddhist author to write on
argument and inference is the idealist Asaṅga (c. 4th
century CE). One passage, often referred to as
Vāda-viniścaya (Settling on what debate
is), occurs in his Abhidharma-samuccaya (Compendium
of the higher teachings) and another, usually referred to as
Hetu-vidyā (Science of grounds), occurs at the
end of a chapter of his
Yogācāra-bhūmi-śāstra (Treatise
on the stages of the practice of yoga). In addition, modern
scholars have ascribed to Asaṅga two other texts which touch on
reasoning but which survive only in Chinese. One is Xiǎn
chàng shèng jiào lùn (Treatise
which reveals and disseminates the wise teachings), whose
Sanskrit title G. Tucci gives as
Prakaraṇa-ārya-vācā-śāstra and
E. Lamotte gives as
Ārya-deśanā-śāstra. The other is
Shùn zhōng lùn (Treatise on following
the middle way), which seems to be a commentary on the
introductory verse of Nāgārjuna’s
Mūla-madhyamaka-kārikā (Katsura 1985:
166).

Shortly after Asaṅga, Vasubandhu (c. 5th century CE),
another Buddhist idealist, thought to be the younger brother of the
Asaṅga, wrote at least three works on debate:
Vāda-hṛdaya (Heart of debate),
Vāda-vidhāna (Precepts of debate) and
Vāda-vidhi (Rules of debate). No Sanskrit
original of any of these survives, though Sanskrit fragments of the
last have been collected by E. Frauwallner (1957). Another work,
ascribed to Vasubandhu, which survives only in Chinese, is
Rú shí lùn (Treatise on truth).
E. Frauwallner conjectures its Sanskrit name to be
Prayoga-sāra, while G. Tucci (1929), when he translated
it back into Sanskrit, gave it the Sanskrit title
Tarka-śāstra, by which it is now generally known.
Finally, there is another work which is only in Chinese. It is
Fāng biàn xīn lùn (Treatise on
the heart of means; T 1632). It is of unknown author and date. G.
Tucci (1929) translated this text too into Sanskrit, giving it the
Sanskrit title, Upāya-hṛdaya.

With the notable exceptions of
Vaiśeṣika-sūtra and
Ṣaṣṭi-tantra, which treat only inference,
an epistemic process, the preponderance of the texts mentioned above
is devoted more to argument in debate than to inference. These texts
typically enumerate, define or classify public discussions,
propositions as they are used in public discussions, parts of
arguments, qualities which either enhance or detract from a
discussant’s performance and statements or actions by a
discussant which warrant his being considered defeated, including the
uttering of various fallacies.

Early polemical Buddhist texts are filled with arguments, many of them
analogical arguments. Particularly replete in such arguments is
Bǎi lùn (Śata-śāstra;
Treatise in one hundred verses) of Āryadeva, a student
of Nāgārjuna.
Though, at this point, there was no accepted, canonical form for
analogical arguments, nonetheless many either have one of the two
forms set out below, or can be easily and faithfully put into one of
them. One form of argument is based on similarity
(sādharmya;
sārūpya).
Such arguments have two premisses: one premiss asserts that two things share a property, the other premiss asserts that one of the two things has a second property. The conclusion asserting that the second thing also has the second property. Arguments by analogy through similarity, then, have this form. The names for the statements have been added for ease of comparison.)

Argument by Analogy Through Similarity

conclusion:

p has S.

ground:

because p has H.

corroboration:

d has H and S.

The other form of argument is based on dissimilarity (vaidharmya; vairūpya). Such arguments also have
two premisses, one asserting that two things fail to share a property and the other asserting that one of them fails to have a second property. Their conclusion asserts that the second thing fails to have the second property. Arguments by analogy through
dissimilarity, then, have this form.

Argument by Analogy Through
Dissimilarity

conclusion:

p does not have S.

ground:

because p does not have H.

corroboration:

d has H and S.

Again, if the argument is not to be circular, p and d
must be distinct. However, here, this follows from the law of
non-contradiction.

Anticipating later discussion, let us see how these two kinds of analogical arguments might be characterized using two terms which become crucial technical terms in Indian logic: namely, subject-like (sa-pakṣa), or similar to the subject, and subject-unlike (vi-pakṣa), or dissimilar to the subject. The Sanskrit prefixes, sa- and vi-, and their respective English adjectives, like and unlike, which are also English prepositions, express the relation of
similarity and dissimilarity respectively. These words express a three
place relation, namely the relation of a thing being like (similar to) or
unlike (dissimilar to) a thing in some respect, but both the Sanskrit
and English expressions, when they are used, permit the
complement referring to the respect in which things are similar or
dissimilar to be left unexpressed. It is this omissibility which
accounts for the fact that the following two sentences are not
contradictory: Devadatta is like Yajñadatta and
Devadatta is unlike Yajñadatta. After all, two
people might be like one another, say, in temperament, but unlike one
another, say, in appearance. The same is true of the Sanskrit
counterparts of these English sentences. When the respect of
similarity or dissimilarity is not expressed in a sentence, it must be
gathered from the context. In Sanskrit, when the context is the
discussion of an argument and no mention is made of the respect in
which the things are similar or dissimilar, it is understood that the
argument's property to be established (sādhya-dharma) is
that with respect to which there is similarity or dissimilarity.

Now, using the technical term, subject-like (sa-pakṣa), one can say that an argument by analogy
through similarity is correct just in case it satisfies two conditions:

first condition:

The existence of the ground (H) in the subject (p).

second condition:

The existence of the ground (H) in a subject-like thing (d).

An important feature of words for similarity in many languages, including English, is the strong pragmatic presumption that things which are alike, or similar, are distinct. If this is true of the Sanskrit words for similarity, then the two conditions just stated
presume that p, the subject of the argument, and d, the corroborating instance, are distinct, thereby excluding circular arguments.

Next, using the technical term, subject-unlike (vi-pakṣa), one can say that an argument by analogy through dissimilarity is correct just in case it satisfies two conditions:

first condition:

The existence of the ground (H) in the subject (p).

third condition:

The non-existence of the ground (H) in a subject-unlike thing (d).

The earliest text to contain an example of an analogical argument in a
canonical form for debate is the Caraka-saṃhitā. Here is one of the two examples (CS 3.8.31) it provides:

Canonical Argument by Analogy

proposition:

the soul is eternal

ground:

because it is un-created,

corroboration:

like space;

application:

as space is uncreated and it is eternal, so is the soul
uncreated;

conclusion:

therefore, the soul is eternal

This form of the argument clearly reflects the debate situation.
First, one propounds a proposition (pratijñā), that is, one sets forth a proposition to be proved. One then states
the ground, or reason (hetu), for the proposition one is
propounding. Next, one corroborates with an example (dṛṣṭānta) which illustrates the connection implicit between the property mentioned in the
proposition and the property adduced as its ground. The immediately ensuing
step, the application (upanaya), spells out the similarity
between the example and the subject of the proposition. Finally, one
asserts the proposition as a conclusion (nigamana).

That the argument is an analogical one is made clear by the use of the
correlative expressions as (yathā) so
(tathā); indeed, the example just given is an argument by analogy through similarity, albeit more prolix in its formulation than the analogical arguments alluded to above. Though Caraka-saṃhitā provides no example of an argument by analogy through dissimilarity in a canonical form, it does refer to the distinction (CS 3.8.36); and
while no examples of arguments at all are found in
Nyāya-sūtra, a pair of examples of analogical
arguments, one through similarity (NS 1.1.33) and one through
dissimilarity (NS 1.1.35), is found in
Nyāya-bhāṣya. The analogical argument in
Caraka-saṃhitā and the argument by analogy through similarity in Nyāya-bhāṣya are essentially
the same, though the parts are grouped together differently.

Canonical Argument By Analogy Through Similarity

proposition:

sound is non-eternal

ground:

because it has the property of arising;

corroboration:

a substance, such as a pot, having the property of arising, is
non-eternal;

application:

and likewise, sound has the property of arising;

conclusion:

therefore, sound is non-eternal because of having the property
of arising,

Canonical Argument By Analogy Through Dissimilarity

proposition:

sound is non-eternal

ground:

because it has the property of arising;

corroboration:

a substance, such as the self, not having the property of
arising, is eternal;

application:

and obversely, sound does not have the property of
arising;

conclusion:

therefore, sound is non-eternal because of having the property
of arising,

As is obvious from such texts, their authors were eager to distinguish
good arguments from bad ones. Not surprisingly, the authors catalogued
bad arguments. Grounds adduced in arguments catalogued as bad are
referred to as non-grounds (a-hetu) or as pseudo-grounds
(hetu-ābhāsa). It is difficult to be sure what the
basis for the classification was. In the case of the
Nyāya-sūtra, the author gives neither a definition
nor an example. Even in cases where definitions and examples are
given, the contemporary reader is not always sure what is intended. In
all likelihood, included here are both cases where the premisses of
the argument can be true but the conclusion false, formal fallacies,
as well as cases where an argument, though formally valid, is
nonetheless unpersuasive, since, for example, its ground
(hetu) is as controversial as its conclusion.

These very same texts, as well as
Vaiśeṣika-sūtra, touch on inference as an
epistemic act. While the examples of inference furnished all have
parts corresponding to a proposition (pratijñā)
and to a ground (hetu), not all the texts are equally
explicit in identifying the form of inference. In particular, both
Caraka-saṃhitā (CS 1.11.21–22) and
Nyāya-sūtra (NS 1.1.5) define inference as
knowledge of one fact on the basis of knowledge of another, leaving
unmentioned any knowledge of a relation linking the two. Moreover,
these texts classify inferences on the basis of characteristics
completely extrinsic to logical features of the inferences adduced.
Inferences appear to be classified according to the temporal order of
the occurrences of the properties of the parts corresponding to a
proposition (pratijñā) and to a ground
(hetu).

Improved definitions, which mention not only the parts corresponding
to a proposition (pratijñā) and to a ground
(hetu) but also the relation between these two parts, are
found in Ṣaṣṭi-tantra and
Vaiśeṣika-sūtra, where knowledge of the
relation is explicitly included in their definitions of inference.
However, the relation is not a formal one, but several from a
miscellany of material relations.
Ṣaṣṭi-tantra enumerates seven such
relations, while Vaiśeṣika-sūtra (VS 9.20)
enumerates five: the relation of cause to effect, of effect to cause,
of contact, of exclusion and of inherence. In each of these texts, the
miscellany of material relations serves to classify inferences. Thus,
although, in these two works, the parts of an inference are made
explicit, the formal connection among these parts remains
implicit.

Another author who is aware that sound inference must be based on a
relation between the proposition and the ground is
Vātsyāyana (5th century CE), also known as
Pakṣalisvāmin, the author of the
Nyāya-bhāṣya. Though, as noted above, the
form of argument he uses has the form of an analogical argument,
Vātsyāyana rejects the mere similarity
(sādharmya-mātra) and the mere dissimilarity
(vaidharmya-mātra), which underlie reasoning by example,
as underlying a sound canonical argument. Vātsyāyana seems
to think that sound canonical arguments are underpinned by the
causation relation. This identification of cause with ground leaves
Vātsyāyana unclear about the difference between obversion and contraposition. (See Gillon 2010 for discussion).

Vasubandhu, a contemporary of
Vātsyāyana, is the first
thinker known to have made clear that the relation, knowledge of which
is necessary for inference, is not just any in a miscellany of
material relations, but a formal one, which he designates, in some places, as
a-vinā-bhāva ---
literally, not being without (cp. the Latin expression sine qua
non) --- and in others, as
nāntarīyakatva --- literally, being
unmediated.

The recasting of the argument form from an analogical argument to a
deductive one seems to have taken place around the time of Vasubandhu.
The earliest record that such a step had been taken is found in
Fāng biàn xīn lùn
(Upāya-hṛdaya) (T 1632 28.1.4), where the
following argument is set out, though without the names of the parts,
which have been added here for the ease of comparison.

A Deductive Argument

proposition:

the self is eternal

ground:

because it is not perceptible by the senses;

corroboration:

space, not being perceptible by the senses, is eternal; that
which is not perceptible by senses is eternal;

application:

the self is not perceptible by senses;

conclusion:

how can the self be non-eternal?

Notice that the third statement consists in two statements, one
a statement to the effect that an instance of something, distinct from
the subject of the argument, has both the ground and the
property to be established, the other to the effect that whatever has
the ground has the property to be established. The former
statement corresponds to the corroboration statement in the argument by analogy through similarity found in the
Nyāya-bhāṣya. The
latter statement is an innovation, which renders the argument a deductively valid one.

Strikingly, the author of Fāng biàn xīn lùn
(Upāya-hṛdaya)
rejects the argument as a bad argument. No other argument in the text is given a canonical form. Moreover, almost all arguments given in the text as examples are analogical ones. Yet, arguments of this deductive form are given as examples of good arguments in Rú shí lùn (Tarka-śāstra),
where the author explicitly rejects analogical arguments as bad arguments.
Moreover, its author justifies this kind of argument by appealing
to a criterion which holds that a proper ground (hetu) (H)
satisfy three forms (tri-rūpa) (T 1633 30.3.18--26). The
first is that the ground (H) occur in the subject (p). The second is
that the ground (H) occur in what is similar (to the subject). The
third is that the ground (H) is excluded from what is dissimilar (to
the subject).

Though there are no texts with passages to this effect, the first and second
forms of a proper ground (tri-rūpa-hetu) could have been
used to characterize an argument by analogy through similarity, while
the first and third forms could have been used to characterize an
analogical argument through dissimilarity. Thus, in an argument by
analogy through similarity, on the one hand, the ground (H)
must occur in the subject of the argument (p) and it must occur
in the example, which itself must be distinct from the subject but
still similar to it insofar as it too must possess the property to be
established (S). In an analogical argument through
dissimilarity, on the other hand, the ground (H) must occur in
the subject of the argument (p) and it must not occur in the
example, which itself must be distinct from the subject and also
dissimilar from it insofar as it does not possess the property to be
established (S). (This paragraph elaborates on a remark made by
Randle (1930: 183) in passing.)

What is clear both from the form of the good arguments and from the
so-called three forms (tri-rūpa) is that a necessary
condition for a canonical argument to be good is this: any choice of a
subject of an argument (p), a ground (H) and a property
to be established (sādhya-dharma) (S) satisfy the
following schema.

Deductive Schema

major premiss:

Whatever has H has S;

minor premiss:

because p has H;

conclusion:

p has S.

It is important to add that satisfaction of this schema is not a
sufficient condition for an argument to be a good one, for such a
schema does not exclude arguments in which the ground (H) and
the property to be established (sādhya-dharma)
(S) are the same; that is to say, it does not rule out circular
arguments, for example.

Though there are no passages to this effect, the first and second
forms of a proper ground (tri-rūpa-hetu) could have been
used to characterize an argument by analogy through similarity, while
the first and third forms could have been used to characterize an
argument by analogy through dissimilarity. Thus, in an argument by analogy through similarity, on the one hand, the ground (H)
must occur in the subject of the argument (p) and it must occur
in the example, which itself must be distinct from the subject but
still similar to it insofar as it too must possess the property to be
established (S). In an argument by analogy through
dissimilarity, on the other hand, the ground (H) must occur in
the subject of the argument (p) and it must not occur in the
example, which itself must be distinct from the subject and also
dissimilar from it insofar as it does not possess the property to be
established (S). (This paragraph elaborates on a remark made by
Randle (1930: 183) in passing.)

As pointed out by H. Ui almost a century ago (Katsura 1985: 166),
neither the canonical argument with a deductive core nor the three
forms of a proper ground characterizing it is original with the author
of Rú shí lùn
(Tarka-śāstra), for these ideas were already
mentioned in Asaṅga’s Shùn zhōng
lùn, though Asaṅga neither endorses the ideas in
this text, nor does he even mention them in either of his two extant
works on argument. If the attribution of Rú shí
lùn (Tarka-śāstra) to Vasubandhu is
indeed correct, then he will turn out to be the first Buddhist author
known to have adopted explicitly as a canonical argument one with a
deductive core and to have used the three forms of a ground
(tri-rūpa-hetu) to justify its form.

4. Classical Period

A clearer and more comprehensive view of inference and argument
emerges in the extant works of Dignāga (c. 5th –
6th century CE) devoted to these topics. Unfortunately, in
each case, the original Sanskrit text has been lost. Two, however, are
extant in Tibetan translation: Hetu-cakra-ḍamaru
(The drum wheel of reason) and his magnum opus,
Pramāṇa-samuccaya (Compendium on epistemic
means of cognition), four of whose six chapters are devoted to
inference and argument. One is extant in both a Chinese and a Tibetan
translation: Nyāya-mukha (Introduction to
logic).

One idea which is particularly clear in Dignāga’s work is
his explicit recognition that inference, the cognitive process whereby
one increases one’s knowledge, and argument, the device of
persuasion, are but two sides of a single coin.

What also emerges in these works is the continued refinement of a
canonical form of argument. Though the texts just mentioned are not
extant in Sanskrit, some of their commentaries are and some of these
texts’ passages are found cited in existing Sanskrit works.
Availing himself of these works, S. Katsura (2004a: 143) has identified
the following as an argument instantiating what Dignāga considers
the canonical form of a good argument.

Canonical Argument for Dignāga

thesis:

sound is non-eternal

ground:

because it results from effort;

similarity corroboration:

that which is immediately connected with an effort is observed
to be non-eternal, like a pot.

dissimilarity corroboration:

that which is eternal is observed not to be immediately
connected with an effort, like space.

Dignāga’s canonical argument differs in four respects from
the sole deductively valid argument, cited above, found in Fāng biàn
xīn lùn (Upaya-hṛdaya). First,
Dignāga’s canonical argument has neither an application
statement nor a conclusion statement. Second, it has two corroboration
statements, instead of one. His first corroboration statement
corresponds to the corroboration statement of the schematic argument by analogy
through similarity and his second corresponds to the corroboration
statement of the schematic argument by analogy through dissimilarity. These
statements come to be known in Sanskrit as statements of
similarity corroboration
(sādharmya-dṛṣṭānta) and of
dissimilarity corroboration
(vaidharmya-dṛṣṭānta) respectively.
Third, each of his two corroboration statements comprises a single
universal statement, though each also includes a phrase referring to an
example which is an instance the universal statement. In other words,
the universal statement in the corroboration statement of the
argument found in Fāng biàn xīn lùn
(Upaya-hṛdaya) is retained and the singular statement
is reduced to what, in English, amounts to a prepositional phrase. We
shall call this phrase the example phrase. Last, Dignāga
seems to have added a word to the canonical form of the corroboration
statement, namely, the word dṛṣṭa
(observed), the past passive participle of the verb
dṛś (to see), which means not only to see
but also to observe, to notice and even to know.

Perhaps most original in Dignāga’s work on argument and inference is what he called wheel of grounds
(hetu-cakra), an equivalent alternative to the three forms of
an argument’s ground. It comprises a three by three matrix,
which distinguishes a proper from an improper ground. It specifies, on the one hand, the three cases of the ground (hetu) occurring in some, none, or all of subject-like things (sa-pakṣa), and, on the other, the
three cases of the ground (hetu) occurring in some, none, or
all of subject-unlike things (vi-pakṣa).
Letting H be the ground, S the subject-like things and \(\bar{S}\) the subject-unlike things, we obtain the following table.

H occurs in:

all \(S\)
all \(\bar S\)

all \(S\)
no \(\bar S\)

all \(S\)
some \(\bar S\)

H occurs in:

no \(S\)
all \(\bar S\)

no \(S\)
no \(\bar S\)

no \(S\)
some \(\bar S\)

H occurs in:

some \(S\)
all \(\bar S\)

some \(S\)
no \(\bar S\)

some \(S\)
some \(\bar S\)

Dignāga identified the arguments corresponding to the top and
bottom cases of the middle column as good arguments and those
corresponding to the other cases as bad.

These developments have led to a rather lively debate among scholars
of the development of logic in early classical India. A very succinct,
but somewhat misleading, way to put the question at the center of the
debate is whether or not Dignāga’s canonical argument is
inductive or deductive. A more cumbersome, but more precise way, to
put the question is this: is there a choice of a subject of an
argument (p), a ground (H) and a property to be
established (sādhya-dharma) (S) which
Dignāga would accept to constitute a good argument but which fail
to satisfy the deductive schema given above. Let us now consider those
aspects of Dignāga’s treatment of argument which are at the
center of this debate.

One reason to doubt that Dignāga would think that arguments
failing to satisfy the deductive schema might nonetheless be good
arguments is the inclusion of the word
dṛṣṭa (observed) in the
corroboration statement. In particular, one might think that
Dignāga would accept as good argument one in which it is not the case that whatever is H is S, but it is the case that
whatever is an observed instance of H is S: that is to
say, the universal statement in the corroboration statement hold only
for observed cases of H, and not for every case of H,
regardless of whether or not the case of H has been observed.
However, no such arguments are accepted by Dignāga. Moreover, the
addition of the word dṛṣṭa
(observed) does not permit attributing such an idea to
Dignāga, for the word is added, not to the corroboration
statement’s subordinate, relative clause, but to its main
clause. Thus, what the universal statement says is, not that every
observed instance of the ground (H) is an instance of the
property to be established (S), but rather that every instance
of the ground (H) is observed to be an instance of the property
to be established (S). Moreover, if the word
dṛṣṭa (observed) has a factive
sense, that is, a sense which presupposes the truth of the clause into
which the word is inserted, as do several of its English translations,
for example, noticed, known, then the word in the
statement leaves the truth conditions of the universal statements un affected.

A further reason which has prompted scholars to doubt that the
good arguments Dignāga had in mind are not ones which would satisfy the
deductive schema is the fact that he has retained an example phrase in
his corroboration statements, for such phrases have no bearing on the
deductive validity of a canonical argument. This doubt is re-enforced
by the fact that statements of similarity corroboration and of dissimilarity
corroboration, stripped of their example phrases, are contrapositives
of another. Thus, one being logically equivalent to the other is also logically superfluous with respect to it. Indeed, Dignāga
seems to be aware of the equivalence, for he acknowledges in his
commentarial discussion of the three forms (PS 2.5) that the second
and third forms are equivalent (Katsura 2000 p. 245; Katsura 2004b pp. 121--124), from which it follows that any two statements, one of which satisfies the second
form and the other of which satisfies the third form are equivalent.

However, perfectly valid deductive arguments are reasonably excluded
as good arguments. Consider, for example, an argument whose conclusion
is identical with one of its premisses. It is a valid argument, though
it is utterly unpersuasive. Dignāga, like any
rational thinker, would not, and did not, accept as a good argument
any argument in which the ground (H) and the property to be
established (S) are the same property, even if such
arguments satisfy the deductive schema. Excluding such circular
arguments is fully consistent with the view that satisfaction of the
deductive schema is a necessary condition on
Dignāga's canonical arguments. (For extensive
scholarly discussion of the role of corroborating instances in
Buddhist arguments, see the collection of articles in Katsura and Steinkellner (eds) 2004.)

A good reason for Dignāga to retain an example phrase in the
corroboration statements of his canonical argument would be to exclude
arguments which are patently unpersuasive, even though, like circular
arguments, they are deductively valid. Consider the following
argument:

thesis:

sound is non-eternal

ground:

because it is audible

corroboration:

whatever is audible is non-eternal.

This argument, rejected as a bad argument by Dignāga, was put
forth by a school of Brahmin thinkers who held, for doctrinal reasons,
that sound is eternal. To maintain this claim in the face of
observation to the contrary, these thinkers maintained instead that
what is transitory is the revelation of sound, not sound itself.
According to them, in other words, sound is constantly present, but we
hear it only when its presence is revealed.

Their argument, though formally valid, is utterly unpersuasive. The
reason is that the instances of audibility (H), are coextensive
with sound (p). Thus, there is no independent empirical
evidence to support the universal statement that whatever is audible
is non-eternal. Requiring that there be at least some thing different
from sound which is both audible and non-eternal is an obvious and
plausible way to eliminate such patently unpersuasive arguments.
Dignāga, therefore,
rules out the argument as a bad argument, rather than, as we would,
accept it as a valid argument with a flawed premiss. (See also Tillemans 1990.)

But this cannot be the entire explanation of why
Dignāga appears to insist on example phrases in
statements of corroboration, for no where does he rule out as a good argument one which, though valid, is unpersuasive for want of some subject-unlike thing.

Because of the doubts just discussed, some scholars think that
Dignāga was not striving work out a deductivist
form of reasoning and argument. Rather, according to some, such as
Hayes (1980; 1988 ch. 4.2), Dignāga was seeking
to develop an inductivist form of reasoning and argument. According to
others, such as Oetke (1994; 1996), Dignāga and
some of his predecessors and contemporaries were striving to spell out
a defeasible form of reasoning and argument. (See Taber 2004 for a
critical assessment of Oetke's view.)

However much scholars may disagree about Dignāga’s aim in
the formulation of the canonical argument, all agree that his works
set the framework within which subsequent Buddhist thinkers addressed
philosophical issues pertaining to inference and debate. Thus,
Śaṅkarasvāmin (c. 6th century CE) wrote a
brief manual of inference for Buddhists, called the
Nyāya-praveśa (Beginning logic), based
directly on Dignāga’s work. Not long thereafter,
Dharmakīrti (c. 7th century CE), the great Buddhist
metaphysician, also elaborated his views on inference and debate
within the framework found in Dignāga.

The canonical argument, conceived of as an inference, is that whereby
one who knows the truth of its premisses may also come to know the
truth of its conclusion. The truth of the premiss corresponding to the
ground, the minor premiss of the deductive schema, is known, of
course, either through perception or through another inference. But
how is the truth of the universal statement of the corroboration
statement, the major premiss of the deductive schema, known? It cannot
be known by inference, since the major premiss is a universal
statement and the conclusion of a canonical argument is a particular
statement. However, to know the truth of the major premiss by
perception would seem to require that one know of each thing which has
H, whether or not it also has S. Yet if one knew that,
one would already know by perception the canonical argument’s
conclusion. As a result, inference would be a superfluous means of
knowledge.

The earliest classical Indian philosopher thought to have recognized
the problem of how one comes to know the major premiss of the Indian
canonical argument seems to have been Dignāga’s student,
Īśvarasena (Steinkellner 1997: 638). He appears to have
thought that knowledge of the canonical argument’s major premiss
is grounded in non-perception (anupalabdhi). That is,
according to Īśvarasena, knowledge that whatever has
H has S comes from the simple failure to perceive
something which has H but which does not have S. (See
Steinkellner 1993, where he draws on Steinkellner 1966).

However, this suggestion does not solve the problem, for reasons laid
out in detail by Īśvarasena’s student,
Dharmakīrti (c. 7th century CE). His extensive writing
on epistemology in general and on reason and argument in particular
formed a watershed in classical India philosophy. Besides his
magnum opus, Pramāṇa-vārttika
(Gloss on the means of epistemic cognition), one of whose
four chapters is devoted to inference
(svārtha-anumāna), comprising 340 verses and a
commentary by him to it, and another devoted to argument
(para-anumāna), which comprises 285 verses, he wrote
several smaller works, including
Pramāṇa-viniścaya (Settling on what the
epistemic means of cognition are), Nyāya-bindu
(Drop of logic), Hetu-bindu (Drop of
reason) and Vāda-nyāya (Logic of
debate). As he makes abundantly clear in verses 13–25 and
his commentary thereto of the chapter on inference
(svārtha-anumāna) of his
Pramāṇa-vārttika, the simple failure to
perceive something which has H but which does not have S
is no guarantee that whatever has H has S; after all,
while one has never encountered something which has H and does
not have S, what guarantee is there that something which has
H and does not have S is not among the things which one
has yet to encounter? Dharmakīrti’s answer was that the
truth of the first premiss is guaranteed by either of two relations
obtaining between properties: causation relation (tadutpatti)
and the identity relation (tādātmya).
Unfortunately, as one might suspect, Dharmakīrti’s solution
does not work. (See Gillon 1991 for details.)

During the time between Dignāga and Dharmakīrti,
thinkers started to add the particle eva to their statement
of the three forms (tri-rūpa) with a view to making it more
precise. (See Katsura 1985.) By the time we reach Dharmakīrti, we see
a formulation of his in which it appears in each of the three
conditions (NB 2.5).

Three Forms of a Ground
(tri-rūpa-hetu)

first form:

the ground's (H) definite (eva) existence in
the subject (p);

second form:

the ground's (H) existence in subject-like things only (eva);

third form:

the ground's (H) utter (eva) non-existence
in subject-unlike things.

Alas, the hoped for precision is undermined by the ambiguity in the meaning of the particle (eva) and of the noun sa-pakṣa (subject-like). This change came in for criticism at the
hands of the Nyāya thinker, Uddyotakara (c. late 6th century CE), and has led to much controvery among contemporary scholars. Let me explain the problem.

The particle eva has two principal uses, one emphatic, the
other restrictive. What it emphasizes or restricts depends on the word
after which it is placed. The particle in the statement of the first form applies to the abstract noun existence and, in its emphatic use, is well translated by definite or actual. The particle in the statement of the third form
applies to the negative abstract noun non-existence and, in its emphatic use with negation, is best translated by utter or at all. (Some scholars translate the particle in these statements as necessary. There is, however,
no philological justification for such a translation.) The particle in the second form particle applies to a concrete noun. Though here the particle could have either an emphatic or a restrictive use, only the restrictive use fits the context. A problem arises from the expression sa-pakṣa)
(subject-likea). As explained earlier, i can be construed in
two ways: either as including or as excluding the subject. If it is
construed as inclusive, then the second and third forms are logically
equivalent and the statement of the three forms has the rhetorical
blemish of containing a logically superfluous form. If it is taken as
exclusive, then the three forms are inconsistent, for in that case the
second form entails the contradictory of the first form. (For full details, see Gillon 1999.)

Ideas on the nature of argument and inference very similar to those of
Dignāga’s are found in works of several of his
contemporaries. For example, in the
Padārtha-dharma-saṃgraha (Summary of
categories and properties), better known as
Praśastapāda-bhāṣya
(Praśastapāda’s commentary, understood as
being a commentary on the Vaiśeṣika-sūtra),
its author, Praśastapāda (c. 6th century CE), an
adherent of the Vaiśeṣika school and a near contemporary of
Dignāga, also clearly viewed the Indian canonical argument as a
formal, valid argument. He made this clear by using the Sanskrit
quantificational adjective sarva (all) to formulate
the second and third conditions of three forms of a ground.(See Randle
1930, ch. 3.1, for discussion.)

Whether or not the view of the canonical argument as a formally valid
one spread from Dignāga to his contemporaries, or from one of his
contemporaries to him, or from some other person predating all of them
has yet to be decided. Whatever the answer is to this question, it is
clear that the canonical argument came to be adopted virtually by
every classical Indian thinker and this same conception, through the
spread of Buddhism, spread to China, Korea and Japan.

It was not long before the ideas on inference and argument became
generally accepted not only by other non-Brahmanical thinkers, such as
the Jains, but also by Brahmanical thinkers. For example, the Jain
thinker, Jinabhadra (6th CE), a junior contemporary of
Dignāga, wrote a commentary on the Jain thinker, Bhadrabāhu,
where he took claims in the latter’s work and recast them in the
form of the canonical argument as found in Dignāga’s work
(Uno 2009.) In addition, one finds that the
Mīmāṃsā thinker, Kumārila Bhaṭṭa
(c. early 7th century CE), adopted, without special
comment, the deductive perspective. His logical ideas are developed at
length in the one hundred eighty-eight verses of his
Śloka-vārttika’s (Gloss in verses)
Anumāna-pariccheda (Section on inference). On
the other hand, one also finds that, though the Nāya thinker, Uddyotakara, argued vigorously against many of Dignāga’s views, he nonetheless advocated a
view which presupposed the same deductive schema as that presupposed
by Dignāga’s works. Thus, Uddyotakara classified grounds
(hetu) as: concomitant (anvaya), where nothing
distinct from particular substratum p (in the inferential
schema) fails to have the property S; exclusive
(vyatireka), where nothing distinct from p (in the
inferential schema) has the property S; and both concomitant
and exclusive, where some things distinct from p have the
property S and some fail to have the property S. This
classification becomes the standard classification for the adherents
of Nyāya during the scholastic period.

While Brahmanical thinkers accepted the insight of the Buddhists that
the canonical inference is underpinned by indispensability, they
refrained from modifying the form of the canonical argument they used.
Rather, the Brahmanical thinkers retained the form of inference found
in Vātsyāyana’s Nyāya-bhāṣya.
However, they understood the steps of corroboration and application to
convey the indispensability relation.

In addition, in spite of the metaphysical differences which
distinguished the various schools of thought, both Buddhist and
Brahmanical, all thinkers came to use a naive realist’s ontology
to specify the states of affairs used to study the canonical argument.
According to this view, the world consists of individual substances,
or things (dravya), universals (sāmānya)
and relations between them. The fundamental relation is the one of
occurrence (vṛtti). The relata of this relation are
known as substratum (dharmin) and superstratum
(dharma) respectively. The relation has two forms: contact
(saṃyoga) and inherence (samavāya). So,
for example, one individual substance, a pot, may occur on another,
say the ground, by the relation of contact. In this case, the pot is
the superstratum and the ground is the substratum. Or, a universal,
say treeness, may occur in an individual substance, say an individual
tree, by the relation of inherence. Here, treeness, the superstratum,
inheres in the individual tree, the substratum. The converse of the
relation of occurrence is the relation of possession.

Another important relation is the relation which one superstratum
bears to another. This relation, mentioned above as indispensability
(a-vinā-bhāṣva), and later known as pervasion
(vyāpti), can be defined in terms of the occurrence
relation. One superstratum pervades another just in case wherever the
second occurs the first occurs. The converse of the pervasion relation
is the concomitance relation.

As a result of these relations, the world embodies a structure: if one
superstratum, designated as H, is concomitant with another
superstratum, designated as S, and if a particular substratum,
say p, possesses the former superstratum, then it possesses the
second. This structure is the one which underlies the classical Indian
canonical argument.

Nyāya-bhāṣya (Commentary on
logic), a commentary on the Nyāya-sūtra, by
Vātsyāyana, who is also known as Pakṣalisvāmin.
Edition: Taranatha and Amarendramohan 1936.
English translation: Jha 1913.
Reference: NSB adhyāya.āhnika.sūtra

Pramāṇa-vārttika (Gloss on epistemic
means of cognition) by Dharmakīrti.
Edition: Pandeya 1989.
English translation: first chapter to verse 38 with autocommentary,
Hayes and Gillon 1991 and Gillon and Hayes 2008; first chapter verses
312 -- 340 with autocommentary, Eltschinger, Krasser and Taber
(trans.) 2012.
English translation of the Chapter on argument: Tillemans 2000.

Pramāṇa-viniścaya (Settling on what
the epistemic means of cognition are) by Dharmakīrti.
Edition of the chapter on perception: Vetter 1966.
Edition of the chapter on inference: Steinkellner 1973.

Praśastapāda-bhāṣya
(Praśastapāda’s Commentary), also known as
Padārtha-dharma-saṃgraha (Summary of
categories and properties), by Praśastapāda.
Edition: Bronkhorst and Ramseier 1994.
English translation: Jha 1916.

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